Giuliani told NBC News anchor Chuck Todd that "truth isn't truth" when trying to make a point about people making contradictory statements in statements to Special Counsel Robert Mueller's investigation.
But Mr Guiliani hit back: "No, it isn't truth".
Mr Giuliani said: "I'm not going to be rushed into having him testify so can he can be trapped into perjury".
Trump has continued to rail against Mueller's probe as a "witch hunt", tweeting before Giuliani's appearance Sunday to compare the investigation to Sen.
CNN anchor John Berman mocked President TrumpDonald John TrumpArizona GOP Senate candidate defends bus tour with far-right activist Alyssa Milano protests Kavanaugh in "Handmaid's Tale" costume Bomb in deadly Yemen school bus attack was manufactured by U.S. firm: report MORE's lawyer Rudy Giuliani on Monday for his declaration that "truth isn't truth". "Not even close", Cuomo said of Trump.
In his MTP chat with Giuliani, Todd suggested the Trump Tower meeting between Donald Trump Jr. and a Kremlin-tied Russian who had promised to bring dirt on Hillary Clinton, should at least be investigated.
The New York Times said it stands by its story.
The very first email Trump Jr. received made explicitly clear that the meeting was predicated on meeting with someone approved of by the Russian government and carrying information provided by that government.
Rudy Giuliani Source Associated Press
"Meanwhile, they're fumbling around with this collusion thing".
He was referring to a conversation former FBI Director James Comey said he had with Trump in the White House in February 2017.
Giuliani argued that the accusations of obstruction of justice against the U.S. president were based on a February 2017 discussion he had with former Federal Bureau of Investigation director James Comey.
In a tweet Monday morning, the president's lawyer said his remark Sunday on "Meet the Press" wasn't a "pontification on moral theology" but a reference to "the classic "he said she said" puzzle". But in explaining why Trump should worry about telling the truth, Giuliani questioned the existence of truth itself. Todd then asked the former Mayor. "Truth isn't truth", Giuliani said. Trump has denied this.
President Donald Trump insisted Sunday that his White House counsel isn't a "RAT" like the Watergate-era White House attorney who turned on Richard Nixon, and he blasted the ongoing Russian Federation investigation as "McCarthyism".
"No, no, no", Giuliani said.
"Truth isn't truth?" Todd replied, adding, "This is going to become a bad meme".
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And that puts Trump's new targeting of Brennan and the others in a much darker light. McRaven's name was not on Trump's list.